The statement from Pyongyang's foreign ministry came the same day North Korea said Kim Jong Un had supervised a test of a "new type of tactical guided weapon with a powerful warhead." Experts have ruled out a long-range missile.
North Korea's call to exclude Pompeo comes a week after the secretary of state agreed Kim is a "tyrant" before a U.S. Senate subcommittee.
On Thursday, North Korea's foreign ministry suggested the reason for the demand is a result of ongoing problems that began in 2018, and Pompeo's "incompatibility" with North Korea regime officials.
"In the future, if dialogue resumes with the United States, we hope someone of mature character with a more easygoing manner of communication will face us in talks," the foreign ministry said.
The ministry added Pompeo scuttled talks in Hanoi, Vietnam.
"Considering the lesson learned in Hanoi, every time Pompeo intervened, work would be hindered and all results would become undone. We fear if Pompeo is involved in talks the situation could again become a mess," North Korea said.
Pyongyang's firing of a new weapon is raising speculation Kim is placing pressure on U.S. President Donald Trump to answer his demands, which include sanctions relief.
China said Thursday North Korea and the United States should make more efforts to ease tensions and build dialogue, Yonhap reported.
Chinese foreign ministry spokesman Lu Kang did not comment on whether Beijing received "advance notice" of the weapon test from Pyongyang, according to the report.
Experts in South Korea say the tested weapon is likely a new cruise missile.
Kim Dong-yup of Kyungnam University told Seoul Pyongyang News North Korea's tactical guided weapon can be launched from ground, air or sea, judging by the description issued by state media.